Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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If F ( X ) = 1 − 1 X , Then Write the Value of F ( F ( 1 X ) ) - Mathematics

If\[f\left( x \right) = 1 - \frac{1}{x}\] , then write the value of \[f\left( f\left( \frac{1}{x} \right) \right)\]

 

 

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Solution

Given:  \[f\left( x \right) = 1 - \frac{1}{x}\]
Now,  \[f\left( \frac{1}{x} \right) = 1 - \frac{1}{\frac{1}{x}} = 1 - x\]

\[\Rightarrow f\left( f\left( \frac{1}{x} \right) \right) = f\left( 1 - x \right)\] Again,
 If \[f\left( x \right) = 1 - \frac{1}{x}\]
Thus, \[f\left( 1 - x \right) = 1 - \frac{1}{1 - x}\] 
\[= \frac{1 - x - 1}{1 - x}\]
\[ = \frac{- x}{1 - x}\]
\[ = \frac{- x}{- \left( x - 1 \right)}\]
\[ = \frac{x}{x - 1}\]
  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 3 Functions
Exercise 3.5 | Q 8 | Page 42
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